Exploration 1

1.First we construct a 120 degree angle three times2.In the first triangle, we make line AC

3.On the second triangle, we make line AC>BC and this makes no triangles because the point C isn't long enough to reach ray A so a triangle could not be formed

4.On the third triangle, we make line BC=AC and this also does not make a triangle because point A is also point C therefore it cannot connect to ray A

The rule is on an obtuse angle, when AC

Exploration 2

1.First we construct three 30 degree triangles and construct a perpendicular bisector on each triangle

2.On the first triangle, we measure the height and draw line BC, making it longer than the height which makes one triangle

3.On the second triangle, we also measure the height and make line BC same is the height which makes one triangle

4.On the third triangle, we make line BC shorter than the height which forms no triangle

The rule is in an acute triangle, when BC>AC then 1 triangle, also when BC=AC then it is also one triangle

Exploration 3

1. First, we draw a 6cm line, 7cm line, 8cm line and a 30 degree angle.

2. Then we construct a 30 triangle, making line AC 7cm (copying the line), and making 2 BC lines that are both 6m long.

3. Then we construct a perpendicular bisector as the height

4. Measure the height

Then we see that we can have 2 triangles when line AC is greater than line BC and this is all greater than the height (AC>BC>h)